K12a225
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+10 q-18+27 q^{-1} -33 q^{-2} +36 q^{-3} -34 q^{-4} +28 q^{-5} -19 q^{-6} +11 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-24 t^2+50 t-63+50 t^{-1} -24 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 z^4+z^2+1 }[/math] |
| Determinant | 227 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-3 z^4 a^6-5 z^2 a^6-2 a^6+3 z^6 a^4+10 z^4 a^4+13 z^2 a^4+5 a^4-z^8 a^2-5 z^6 a^2-12 z^4 a^2-12 z^2 a^2-4 a^2+z^6+3 z^4+4 z^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+5 a^6 z^{10}+10 a^4 z^{10}+5 a^2 z^{10}+10 a^7 z^9+25 a^5 z^9+24 a^3 z^9+9 a z^9+10 a^8 z^8+19 a^6 z^8+15 a^4 z^8+14 a^2 z^8+8 z^8+5 a^9 z^7-9 a^7 z^7-48 a^5 z^7-49 a^3 z^7-11 a z^7+4 z^7 a^{-1} +a^{10} z^6-20 a^8 z^6-65 a^6 z^6-80 a^4 z^6-53 a^2 z^6+z^6 a^{-2} -16 z^6-9 a^9 z^5-12 a^7 z^5+16 a^5 z^5+26 a^3 z^5-a z^5-8 z^5 a^{-1} -a^{10} z^4+13 a^8 z^4+58 a^6 z^4+86 a^4 z^4+57 a^2 z^4-2 z^4 a^{-2} +13 z^4+4 a^9 z^3+13 a^7 z^3+11 a^5 z^3+2 a^3 z^3+5 a z^3+5 z^3 a^{-1} -3 a^8 z^2-19 a^6 z^2-35 a^4 z^2-27 a^2 z^2+z^2 a^{-2} -7 z^2-3 a^7 z-5 a^5 z-3 a^3 z-2 a z-z a^{-1} +2 a^6+5 a^4+4 a^2+2 }[/math] |
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